The modified successive approximations method and Padé approximants for solving the differential equation with variant retarded argument
type: Item
instance of: scholarly article
title: The modified successive approximations method and Padé approximants for solving the differential equation with variant retarded argument
zbMATH Open document ID: 1055.65088
DOI: 10.1016/S0096-3003(03)00349-7
author: Ercan Çelik
author: Arzu Aykut
author: Mustafa Bayram
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: In order to approximate the solution of the boundary-value problem for a linear second-order delay differential equation, \[ \begin{gathered} x''(t)+ a(t) x(t-\tau))= f(t),\quad t\in [0,T],\\ x(t)= \varphi(t),\quad t\leq 0,\quad x(T)= x_T,\end{gathered} \] the authors convert the problem into a mixed (Fredholm-Volterra type) integral equation. Approximations to \(x\) are then obtained by iterative techniques based on successive approximation and series of Padé approximants. A test problem illustrates the method.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 2081696
zbMATH Keywords: boundary-value problem
zbMATH Keywords: retarded argument
zbMATH Keywords: Fredholm-Volterra integral equation
zbMATH Keywords: successive approximation
zbMATH Keywords: numerical example
zbMATH Keywords: Padé approximants
zbMATH Keywords: linear second-order delay differential equation
Wikidata QID: Q115339726
reviewed by: H. Brunner
MaRDI profile type: Publication
cites work: Q5642900
cites work: Q3994364
cites work: The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation
cites work: On the numerical solution of differential-algebraic equations by Padé series
full work available at URL: s0096-3003(03)00349-7
OpenAlex ID: W4241913648
description: scientific article; zbMATH DE number 2081696